摘要:

We prove a posteriori error bounds and convergence of Rayleigh-Schrödinger Series for bases of maximal invariant subspaces of compact operators in Banach spaces. These results generalize those for eigenvectors associated with simple eigenvalues. Recursive formulae are given for the numerical computation of the series' coefficients.

ISSN:0163-0563    

DOI:10.1080/01630569108816406

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

Numerical computation of Rayleigh-Schrödinger Series for maximal invariant sub-spaces is done for compact integral operators with defective eigenvalues. The series are applied to refine iteratively an approximate starting basis. The integral operators are discretized by different approximation methods which are known to be a strongly stable approximations at any nonzero eigenvalue. Rayleigh-Schrödinger Series are compared with three inexact Newton methods that perform the same goal.

ISSN:0163-0563    

DOI:10.1080/01630569108816407

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630569108816408

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

Let E be a closed set of the Banach space X and Lp(I,E) be the space of all p–Bochner integrable functions with domain (I,m), I =[0,1] and m the Lebesgue measure on I, and with essential range in E. In the second part of this paper we study the proximinality of the set Lp(I,E) in Lp(I,X), 1≤p≤∞.

ISSN:0163-0563    

DOI:10.1080/01630569108816409

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630569108816410

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

This paper is concerned with the application of implicit Runge-Kutta methods suitable for stiff initial value problems to initial value problems for differential inclusions with upper semicontinuous right-hand sides satisfying a uniform one-sided Lipschitz condition and a growth condition. The problems could stem from differential equations with state discontinuous right-hand sides. It is shown that there exist methods with higher order of convergence on intervals where the solution is smooth enough. Globally we get at least the order one.

ISSN:0163-0563    

DOI:10.1080/01630569108816411

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

We discuss initially how to construct a generalisation of the Lebesgue-Bochner function spaces by using a Banach lattice of real-valued functions and an appropriate lifting of the norm from this space to the more general setting. This lifting is shown to be well-defined, but the primary purpose is to discuss the notion of proximinality in this new space. In this paper, the results are derived by establishing the property of uniform convexity under suitable hypotheses. Other techniques may be found in the literature, and citations are given in the paper.

ISSN:0163-0563    

DOI:10.1080/01630569108816412

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

We study uniform approximation by functions belonging to a classK0=K∩Rs, whereSis an arbitrary nonempty setis closed under pointwise supremum andK0remains invariant under addition with constants. In particular, we obtain a sufficient condition for the greatest best approximation selection to have 2 as its least Lipschitz constant. We also characterize those functions which are at a finite distance fromK0, whenK0is the family of convex or quasiconvex or N–Lipschitz functions or the intersection of any two of these families.

ISSN:0163-0563    

DOI:10.1080/01630569108816413

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

We discuss the classical notions of capacity, transfinite diameter, Chebyshev constant and equilibrium distributions in the context of locally compact spaces. We also demonstrate how the analogues of certain theorems in classical potential theory can be extended to this framework and applied to various problems in approximation theory. In particular, we explore the similarities between the theory of weighted polynomials and the theory of radial basis functions from a potential theoretic perspective.

ISSN:0163-0563    

DOI:10.1080/01630569108816414

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

This paper presents a new algorithm for solving the optimal control problems with control constraint. The special feature of the algorithm lies in the fact that the function to be minimized is the Hamiltonian function plus some penalty terms for the variation of the control, and that the convexity assumption for the control domain is not needed. It is proved that the sequence of controls and states constructed by the algorithm satisfies the Pontryagin maximum principle asymptotically.

ISSN:0163-0563    

DOI:10.1080/01630569108816415

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor